Question

Galileo attempted to measure the speed of light by measuring the time elapsed between his opening a lantern and his seeing the light return from his assistant's lantern. What distance, d, must separate Galileo and his assistant in order for the human reaction time, Δt = 0.2 s, to introduce no more than a 14 % error in the speed of light? Answer in meters.

Answer 1

Answer:

The distance is $2.58\times10^{7}\ m$.

Explanation:

Given that,

Time $\Delta t = 0.2\ s$

The velocity is no more than a 14 % error in the speed of light.

So,

Velocity $v= c\times 86\%$

We need to calculate the distance

Using formula of speed

$v = \dfrac{d}{t}$

$d = v\times t$

Where, v = speed

d = distance

t = time

Put the value into the formula

$d = 3\times10^{8}\times\dfrac{86}{100}\times0.2$

$d=516\times10^{5}\ m$

We know that,

The one side distance d' is

$d'=\dfrac{d}{2}$

$d'=\dfrac{516\times10^{5}}{2}$

$d'=2.58\times10^{7}\ m$

Hence, The distance is $2.58\times10^{7}\ m$.